Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in JAVA):

Solution:
import java.util.*;

public class Main
{
    public static void main(String[] args)
    {
        double ans = 0.0;
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        List<Double> x=new LinkedList<>();
        for (int i = 0; i < n; ++i) { x.add(sc.nextDouble()); }
        double max=Double.MIN_VALUE;
        Collections.sort(x);


        for (int i=0;i<n-1;++i)
        {
            double res=0.0;
            int c=i+1;
            int a=n-1;
            int b=n-2;
            if (i==n-3) { b=i-1;}
            else if (i==n-2)
            {
                a=i-1;
                b=i-2;
            }
            res=(x.get(a)+x.get(b))/(x.get(c)-x.get(i));
            if (max<res) {max=res;}
        }

        System.out.println(String.format("%.7f",max));
    }
}